(x-1)(x+7)=-15

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Solution for (x-1)(x+7)=-15 equation: 


Simplifying
(x + -1)(x + 7) = -15

Reorder the terms:
(-1 + x)(x + 7) = -15

Reorder the terms:
(-1 + x)(7 + x) = -15

Multiply (-1 + x) * (7 + x)
(-1(7 + x) + x(7 + x)) = -15
((7 * -1 + x * -1) + x(7 + x)) = -15
((-7 + -1x) + x(7 + x)) = -15
(-7 + -1x + (7 * x + x * x)) = -15
(-7 + -1x + (7x + x2)) = -15

Combine like terms: -1x + 7x = 6x
(-7 + 6x + x2) = -15

Solving
-7 + 6x + x2 = -15

Solving for variable 'x'.

Reorder the terms:
-7 + 15 + 6x + x2 = -15 + 15

Combine like terms: -7 + 15 = 8
8 + 6x + x2 = -15 + 15

Combine like terms: -15 + 15 = 0
8 + 6x + x2 = 0

Factor a trinomial.
(4 + x)(2 + x) = 0


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Simplifying
x = -2
Solution
x = {-4, -2}

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